I don’t know about “most” important, but in soccer, the ref can stop play due to a serious head injury (even if there was no foul committed or other reason to stop play). Technically, play restarts with a drop ball where the ball is live as soon as it hits the ground, so both teams could theoretically contest the drop ball. But the unwritten rule is that if one team obviously had possession at the time, they get to keep the ball off the drop ball. I think this is important because otherwise, a team could be penalized (by losing possession to the other team) because the ref decided to stop play to ensure player safety.

Least important? Anything related to running up the score in top level competition. As long as players on the winning / losing team are playing with respect (not, you know, trying 360 dunks or bat flipping on home runs for no reason), if they continue to score points / goals in a game that is over, who cares – especially in leagues where point differential / goals scored matters, and those extra points could matter at the end of the season.